Pairwise Correlations in Layered Close-Packed Structures

TL;DR

This paper develops analytical formulas for pairwise correlation functions in layered close-packed structures modeled by hidden Markov models, enabling efficient computation and revealing new relations.

Contribution

It provides explicit analytical expressions for correlation functions in layered structures modeled by hidden Markov models, enhancing computational efficiency and understanding.

Findings

Analytical formulas match previous results

New relations between correlation functions derived

Efficient computation of correlation functions achieved

Abstract

Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated analytically as explicit functions of model parameters or the expressions may be used as a fast, accurate, and efficient way to obtain numerical values. We present several examples, finding agreement with previous work as well as deriving new relations.